The expression in problem 39 is:

$\sqrt{50x} - \sqrt{8x}$

To simplify this, we first factor out the square roots where possible.

1. Factor inside the square roots:
   • $\sqrt{50x} = \sqrt{25 \cdot 2x} = \sqrt{25} \cdot \sqrt{2x} = 5\sqrt{2x}$
   • $\sqrt{8x} = \sqrt{4 \cdot 2x} = \sqrt{4} \cdot \sqrt{2x} = 2\sqrt{2x}$

Now substitute the simplified terms back into the expression:

$5\sqrt{2x} - 2\sqrt{2x}$

Since both terms have $\sqrt{2x}$ as a common factor, we can combine them:

$(5 - 2)\sqrt{2x} = 3\sqrt{2x}$

Thus, the simplified form of the expression is:

$3\sqrt{2x}$

Would you like more details or have any questions? Here are 5 related questions to expand on this topic:

1. How do you simplify square roots with variables?
2. What is the process for combining like terms in radical expressions?
3. Can you simplify expressions with higher-order roots (like cube roots) similarly?
4. How do you handle square roots when variables are squared inside the radical?
5. Can you explain how to rationalize the denominator when radicals are involved?

Tip: Always check if the numbers inside the square root can be factored into perfect squares to simplify the expression efficiently.